Irreversible classical dynamics and quantum chaos

Quantum statistical properties of systems which are chaotic in their classical limit can be described within the framework of an effective field theory. Within this description, spectral properties are expressed in terms of an effective action involving the low lying relaxation modes of the irreversible classical evolution operator. We critically review the development and application of this general field theoretic approach. In doing so, parallels will be drawn between the general properties of quantum chaotic structures and weakly disordered conductors.